Temporary Cohabitation: The Metastable Phase Au4Si

The prediction, identification, and characterization of phases away from equilibrium conditions remain difficult challenges for material science. Herein, we demonstrate how systems whose phase diagrams contain deeply incising eutectics can offer opportunities to address these challenges. We report the synthesis of a new compound in the Au–Si system, a textbook example of a system with a deep eutectic. Au4Si crystallizes in a complex √18×√2×1 superstructure of the PtHg4 type, based on the distortion of vertex-sharing Si@Au8 cubes into bisdisphenoids. Au4Si decomposes upon heating and at room temperature even in high vacuum, highlighting its metastability. Electronic structure analysis reveals a pseudogap at the Fermi energy, which is enhanced by the superstructure through the relief of Au–Au antibonding interactions. The pseudogap is associated with a Zintl-type bonding scheme, which can be extended to the locally ordered liquid. These results highlight the potential for metastable phases to form in deep eutectics that preserve the local structures of the liquid.


Thermal analysis
3. Crystallographic data from single-crystal X-ray diffraction data 4. Crystal chemical and symmetry relations 5. Transmission electron microscopy and energy-dispersive X-ray spectroscopy 6. Physical properties 7. Computations 8. References

Preparation
Sample handling, except for diffraction experiments, and storage were conducted in an argonfilled glove box (MBraun, H2O<0.1 ppm, and O2<0.6 ppm). The samples were synthesized from pure Au and Si using an arc melter (Edmund Bühler GmbH, MAM-1) in argon atmosphere. All sample transfer was conducted in argon-filled containers. Differential Scanning Calorimetry (DSC) was performed in a NETZSCH DSC 214 with a concave Al pan and a pierced lid between 20 and 550°C and heating and cooling rates of 10 K min -1 (sample mass 111.6 mg) in argon atmosphere and between -50 and 300°C in a DSC Q2000 device with heating and cooling rates of 10 K min -1 (sample mass 25.568 mg) and nitrogen atmosphere in an Al pan and lid. Simultaneous Thermal Analysis with simultaneous application of Thermogravimetry (TG) and DSC was performed in a NETZSCH STA 449F3 with an Al2O3 DSC/TG pan between 30 and 1400°C with a heating rate of 10 and a cooling rate of 40 K min -1 (sample mass 164.1 mg) in argon atmosphere.

Thermal analysis
DSC measurements of Au4Si in argon and nitrogen atmosphere ( Figure S1) reveal an exothermic effect with Tonset = 495(10) K, which is in sound agreement with findings in [1]. This effect could denote a phase transition to a high-temperature phase of Au4Si or the recrystallization of elemental Au. Since the quenching of this possible high-temperature phase was not achieved, insitu temperature-dependent X-ray diffraction experiments were conducted (see paragraph 3). A corresponding signal upon cooling, as well as in the second heating cycle that could denote the reformation of Au4Si is not observed. Upon further heating, an endothermic effect at Tonset =

Temperature-dependent diffraction experiments on single crystals in air and sealed in capillaries
under argon atmosphere revealed that the exothermic effect with Tonset = 495(10) K visible during DSC and STA experiments is assigned to a partial decomposition into polycrystalline Au upon heating. Nevertheless, the Au4Si structure is also stable at higher temperatures and was detected for ~4 min at the maximum investigated temperature of 573 K.

Transmission electron microscopy and energy-dispersive X-ray spectroscopy
The compound was investigated using a JEOL 3000F analytical high-resolution transmission electron microscope with a field-emission electron source, operated at 300 kV. The microscope is equipped with a Gatan Orius camera (point-to-point resolution: 0.17 nm in TEM mode). The energy dispersive X-ray spectroscopy analysis was performed with an Oxford X-MAX XEDS system with an 80 mm 2 SDD detector. Imaging and analyses were conducted in a low-background beryllium double-tilt holder.
In-situ observation of changes of the samples upon heating in the transmission electron microscope was prevented by the instability of particles with appropriate thickness in the beam.  The molar susceptibility χM ( Figure S5) denotes diamagnetic behavior and remains constant between 260 and 400 K as well as between 160 and 260 K but at a slightly smaller value. The sum of the diamagnetic increments for Au and Si [24] amounts to Σincr = -924.2 × 10 -6 emu mol -1 , which is in fair agreement with the measured values. Below 160 K, an upturn denoting minor paramagnetic impurity  The specific heat Cp(T) of Au4Si ( Figure S6) shows a complex trend with a transition at Tonset=260 K and Tmid=295(5) K, taken from the first derivative of the specific heat Cp(T). DSC measurements in the temperature range from 185 to 310 K do not denote a phase transition ( Figure S1, left, inset) and therefore, the observed slight variation in heat capacity near room temperature could be caused by the grease used to adhere the sample to the holder. The data are sufficiently described by the empirical formula Cp=a+bT+cT 2 +dT 3 [25] with the constants derived from the fits listed in Table S4.
The Debye temperature θD [25,26] amounts to 254 K at low temperatures (2<T<210 K), 210 K at higher temperatures (200<T<400 K) and 289 K for the whole measured range (2<T<400 K), respectively (Table S4). The value for the higher temperature range is in sufficient agreement with the one previously reported for a mixture Au81.4Si18.6 (θD=220 K [2]), but is smaller than the experimental value derived from low-temperature data. The latter one is in good agreement with the value estimated from Neumann-Kopp's rule for eutectic mixtures [27] 259 K (at 0K [28]).

Computational Procedures and Details
Electronic Structure Analysis: Structure optimization and the calculation of total energies, band energies, and density of states (DOS) distributions were performed for all Au4Si structure variants using the Vienna ab initio Simulation Package (VASP) [29][30][31][32]. Calculations utilized the Projector Augmented Wave (PAW) [33,34] potentials and the Generalized Gradient Approximation (GGA) [35,36] in high precision mode. The computational parameters for these calculations are detailed in Table S5. Each structure was first geometrically optimized (Tables S6, S8-S10) before a single-point calculation was performed to generate the DOS distributions, electronic band energies, and total energies (Table S13). DOS curves were drawn with viewkel (a part of YAeHMOP) [37]. To better visualize the electronic structures, the degeneracy at the k-points of interest was broken by a slight modification of the atomic position of Si, as well as an alteration of the cell dimensions (Tables S7, S11-S12); these changes did not have a significant impact on the band structures generated ( Figure S7).
The GGA-DFT electronic structure was used as the basis for the calibration of a simple Hückel model for investigation with the reversed approximation Molecular Orbital method [38]. The projected DOS distributions and band energies were used as reference data for the refinement of the semi-empirical parameters of the Hückel model with the eHtuner program [39]. The basis set consists of Slater-type orbitals corresponding to the Si 3s, Si 3p, Au 6s, and Au 6p atomic orbitals, along with double-ζ functions for the Au 5d. With the resulting parameters (Table S14) To examine the potential influence of spin-orbit coupling (SOC), electronic structure calculations were performed with LDA-DFT using the ABINIT [40][41][42] package and Hartwigsen-Geodecker-Hutter norm-conserving pseudopotentials [43] for each of the three Au4Si structure types. The structures were optimized with a two-step approach: first, the unit cell was held fixed while the atomic positions were optimized, then all parameters were relaxed simultaneously. Once the structures were optimized, DOS calculations were performed, both with and without SOC ( Figures S8-S10). The features of the DOS near the Fermi energy are largely unchanged by the introduction of SOC.  give the corresponding band structures for phases in which the symmetry is weakly broken to remove band degeneracies.